# st: Re: Monte Carlo Simulation for Heteroskedastic Tobit Model

 From Sachin Chintawar To statalist@hsphsun2.harvard.edu Subject st: Re: Monte Carlo Simulation for Heteroskedastic Tobit Model Date Thu, 16 Apr 2009 15:41:06 -0600

```Dear all
First
Thank you Martin & other statalist users

Well I did find the book very helpful. Find a program that I have been
able to now develop. But has a few problems
clear all

quietly set obs 30
global numobs 100             // sample size N
global numsims "1000"         // number of simulations
set seed 678643594

program tobit, rclass
version 10.1
drop _all
set obs \$numobs
scalar a = 0
scalar b = 12
scalar mu = 5
scalar sigma = 4
generate u= runiform()
generate y=normal((a-mu)/sigma)+u*(normal((b-mu)/sigma)-normal((a-mu)/sigma))
generate ytrunc = mu + sigma*invnorm(y)
generate x = rnormal()

regress ytrunc x
return scalar b2 = _b[x]
return scalar se2 = _se[x]
return scalar t2 = (_b[x]-2)/_se[x]
return scalar r2 = abs(return(t2))> invttail(\$numobs-2,.025)
return scalar p2 = 2*ttail(\$numobs-2,abs(return(t2)))
end

simulate b2r=r(b2) se2r=r(se2) t2r=r(t2) reject2r=r(r2) p2r=r(p2), ///
reps(\$numsims): tobit
mean b2r se2r reject2r

My Questions now are:
1. Since I had generated 'ytrunc' as a truncated normal distribution,
then to know the bias I cannot tell stata to generate 'ytrunc' based
on a equation such as
y = b1 + b2*x + u
where b1 and b2 are specified. But if I do this then y goes to
having a normal distribution and not a truncated normal distribution.

2. Another problem is to develop a heteroskedastic error term. Can I
develop that using
generate u= runiform() * c*z_factor

Where c is a constant varying from 0.1 to 1.0 and the
z_factor changes for each 'i' - then how do I define the z_factor?

I would greatly appreciate any pointers that you could provide me in this regard

Sincerely
Sachin
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```